Abstract

Classical multivariate analysis techniques such as principal components analysis (PCA), canonical correlation analysis (CCA) and discriminant analysis (DA) can be badly affected when extreme outliers are present. The purpose of this thesis is to present new robust versions of these methods. Our approach is based on the following observation: the classical approaches to PCA, CCA and DA can all be interpreted as operations on a Gaussian likelihood function. Consequently, PCA, CCA and DA can be robustified by replacing the Gaussian likelihood with a Cauchy likelihood. The performance of the Cauchy version of each of these procedures is studied in detail both theoretically, through calculation of the relevant influence function, and numerically, through numerous examples involving real and simulated data. Our results demonstrate that the new procedures have good robustness properties which are certainly far superior to these of the classical versions.